Movement of displacers in most prior art Vuilleumier heat pumps are synchronized via a crank, such as shown in U.S. Pat. No. 1,275,507. A schematic of such a heat pump with crank-synchronized displacers is shown in FIG. 1. In the '507 patent, the displacers have a phase difference of 90 degrees as shown in FIG. 2. A mechatronically-driven Vuilleumier heat pump, which is commonly assigned to the assignee of the present disclosure, has been disclosed in WO 2013/155258. In such a heat pump, the displacers are independently actuated allowing one displacer to remain stationary while the other displacer moves, which provides many additional degrees of freedom in controlling displacer motion. In the WO 2013/155258 A1 publication, a three-process cycle is also disclosed. A cycle that provides a high coefficient of performance is desired. Furthermore, it is desirable to have a cycle that provides a high coefficient of performance at a range of demand levels, i.e., demand for heating or cooling.
In U.S. Pat. No. 5,301,506, a cycle is discussed for theoretical discussion purposes. “The thermodynamic operation . . . may be better understood with reference to the example discussed below of a machine having intermittent displacer motions.” Later in the same paragraph: “It will be appreciated that, in practice, theoretically ideal conditions will not be obtainable.” In the '506 reference, a thermodynamic analysis of a cycle in which displacer movement can be intermittent is analyzed. Because the inventor of the '506 reference has not contemplated an apparatus to provide such intermittent movement, the practicalities involved in operating such an apparatus are not considered.